Jump inequalities via real interpolation
By Mariusz Mirek, E. Stein, Pavel Zorin-Kranich. Mathematische Annalen, 2018
47 citations recorded by the source corpus.
Jump inequalities are the $$r=2$$ r = 2 endpoint of Lépingle’s inequality for r -variation of martingales. Extending earlier work by Pisier and Xu (Probab Theory Relat Fields 77(4):497–514, 1988 ) we interpret these inequalities in terms of Banach spaces which are real interpolation spaces. This interpretation is used to prove endpoint jump estimates for vector-valued martingales and doubly stochastic operators as well as to pass via sampling from $$\mathbb {R}^{d}$$ R d to $$\mathbb {Z}^{d}$$ Z d for jump estimates for Fourier multipliers.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e64ec67c01dbdda1196ad73821158933419264b4
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In Applied Mathematics
- Mariusz Mirek
- Terence Tao
- Sanghyuk Lee
- D. Tataru
- Zihua Guo
- Carlos E. Kenig
- Jonathan Bennett
- Shuanglin Shao
In Mathematical Physics
Citations in the corpus
- Pointwise ergodic theorems for non-conventional bilinear polynomial averages (2020, background): “‖F‖Lp1 (AZ)‖G‖Lp2 (AZ) 9See for instance [57] for an overview of this interpolation theory.”